Are there any schools that do both Scholar's Cup and Academic Decathlon? What is that like?

There are a fair few in LA, Houston, and Dallas. I can't speak to it personally but as someone who is involved with both WSC and DemiDec, the ethos of WSC is much more about curiosity + independent learning. The students who do well will probably be ones who are comfortable with intellectual uncertainty, critical thinking, and less structured environments.

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Another way of looking at it: AD asks for the right answer based on the resource guide; WSC asks for the best answer based on the options available.